基于微分平坦的板球系统反步滑模控制  

Backstepping Sliding Mode Control of Ball-and-Plate System Based on Differential Flatness

作　　者：韩光信[1] 王嘉伟 胡云峰[2] HAN Guangxin;WANG Jiawei;HU Yunfeng(College of Information and Control Engineering,Jilin of Chemical Technology,Jilin 132022,China;College of Communication Engineering,Jilin University,Changchun 130012,China)

机构地区：[1]吉林化工学院信息与控制工程学院,吉林吉林132022 [2]吉林大学通信工程学院,长春130012

出　　处：《吉林大学学报（信息科学版）》2024年第2期260-268,共9页Journal of Jilin University（Information Science Edition）

基　　金：国家自然科学基金青年基金资助项目(61703177)。

摘　　要：为改善板球系统轨迹跟踪控制误差大,控制精度低的问题,提出了一种基于微分平坦的板球系统反步滑模控制方法。首先基于欧拉-拉格朗日方程建立板球系统的运动学模型,通过合理简化得到解耦线性状态空间模型。以X轴方向控制器设计为例,利用微分平坦技术获得系统的目标状态量以及前馈控制量,建立误差系统,进而采用反步法实现对误差系统的滑模控制,利用李雅普诺夫稳定性理论证明了闭环系统的稳定性。算法中使用双曲正切函数抑制滑模的抖动,实现了对板球系统的轨迹高精度跟踪控制。仿真实验结果表明,该方法控制精度高,具有良好的控制效果。In order to improve the problem of large trajectory tracking control error and low control accuracy of ball and plate system,a differential flatness-based backstepping sliding mode control method is proposed for enhancing the tracking accuracy in ball and plate system.Firstly,based on the Euler-Lagrange equation,the kinematic model of ball and plate system is established,the decoupled linear state-space model is obtained by reasonable simplification.Taking the X-direction controller design as an example,the target state quantity and feedforward control quantity of the system are obtained by using differential flatness technology,and an error system is constructed.Then,the backstep method is used to realize the sliding mode control of the error system,and the stability of the closed-loop system is proved by Lyapunov stability theory.The hyperbolic tangent function is used in the algorithm to suppress the jitter of the sliding mode,and the trajectory tracking control of ball and plate system is realized with high accuracy.Simulation results show that the proposed control strategy has high control accuracy and better control performance.

关 键 词：板球系统 轨迹跟踪 微分平坦 反步滑模控制 双曲正切函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]